Commit 4081931a authored by Michael Wimmer's avatar Michael Wimmer

fix more math

parent 437023a7
Pipeline #43789 passed with stages
in 1 minute and 15 seconds
......@@ -489,12 +489,12 @@ the eigenfunctions of $L$.
Recall that q quantum state $|\phi\rangle$ can be written in an orthonormal
basis $\{ |u_n\rangle \}$ as
$$\|\phi\rangle = \underset{n}{\Sigma} \langle u_n | \phi \rangle\, |u_n\rangle.$$
$$|\phi\rangle = \underset{n}{\Sigma} \langle u_n | \phi \rangle\, |u_n\rangle.$$
In terms of hermitian operators and their eigenfunctions, the eigenfunctions
play the role of the orthonormal basis. In reference to our running example,
the 1D Schrödinger equation of a free particle, the eigenfunctions
$\sin(\frac{n \pi x}{L})$ play the role of the basis functions $\ket{u_n}$.
$\sin(\frac{n \pi x}{L})$ play the role of the basis functions $|u_n\rangle$.
To close our running example, consider the initial condition
$\psi(x,o) = \psi_{0}(x)$. Since the eigenfunctions $\sin(\frac{n \pi x}{L})$
......@@ -583,7 +583,7 @@ necessary to work with numerical methods of solution.
6. [:sweat:] We consider the Hilbert space of functions $f(x)$ defined
for $x \ \epsilon \ [0,L]$ with $f(0)=f(L)=0$.
Which of the following operators on this space is hermitian?
Which of the following operators on this space is Hermitian?
(a) $L = A(x) \frac{d^2 f}{dx^2}$
......
Markdown is supported
0% or
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment